Schroedinger Operator with Strong Magnetic Field: Propagation of singularities and sharper asymptotics

Abstract

We consider 2-dimensional Schrödinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o({\mu }^{-1}{h}^{-1})$ or better. We also consider 3-dimensional Schrödinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o({\mu }^{-1}{h}^{-1})$ or better. We also consider generalized Schrödinger-Pauli operator in the same framework albeit with $\mu h\ge 1$ and derive spectral asymptotics with the remainder estimate up to $O(h^{-1}|\log h|)$ and with the principal part $\asymp \mu h^{-2}$.

19 pp, 10 figs